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Abstract: . The initial-algebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying different ways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursive pattern of computation on those objects, which is very helpful for both functional and parallel programming. We show how to model a particular kind of directed acyclic graph using this... (Update)
Context of citations to this paper: More
...folds for abstract data types has been almost neglected so far. Despite proposals for specific types, such as arrays [1] or graphs [8, 2], it is only Fokkinga [7] who attacks the problem from a general point of view. In his approach terms are represented by combinators,...
...it lacks efficiency since direct access to a node requires, in general, traversal of the whole graph. Also related is the work of Gibbons [11] who considers the definition of graph fold operations within an algebraic framework. But he deals only with acyclic graphs, and an...
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3: Revisiting Catamorphisms over Datatypes with Embedded Functions - Fegaras, Sheard - 1996
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BibTeX entry: (Update)
J. Gibbons. An Initial Algebra Approach to Directed Acyclic Graphs. In Mathematics of Program Construction, LNCS 947, pages 282--303, 1995. http://citeseer.ist.psu.edu/article/gibbons95initialalgebra.html More
@incollection{ gibbons95initialalgebra,
author = "Jeremy Gibbons",
title = "An Initial-Algebra Approach to Directed Acyclic Graphs",
booktitle = "Proceedings 3rd Int.\ Conf.\ on Mathematics of Program Construction, {MPC}'95, Kloster Irsee, Germany, 17--21 July 1995",
volume = "947",
publisher = "Springer-Verlag",
address = "Berlin",
editor = "B. M{\"o}ller",
pages = "122--138",
year = "1995",
url = "citeseer.ist.psu.edu/article/gibbons95initialalgebra.html" }
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